Highly Tunable Electrostatic Nanomechanical Resonators

There has been significant interest towards highly tunable resonators for on-demand frequency selection in modern communication systems. Here, we report highly tunable electrostatically actuated silicon-based nanomechanical resonators. In-plane doubly-clamped bridges, slightly curved as shallow arches due to residual stresses, are fabricated using standard electron beam lithography and surface nanomachining. The resonators are designed such that the effect of mid-plane stretching dominates the softening effect of the electrostatic force. This is achieved by controlling the gap-to-thickness ratio and by exploiting the initial curvature of the structure from fabrication. We demonstrate considerable increase in the resonance frequency of nanoresonators with the dc bias voltages up to 108% for 180 nm thick structures with a transduction gap of 1 $mu$ m separating them from the driving/sensing electrodes. The experimental results are found in good agreement with those of a nonlinear analytical model based on the Euler-Bernoulli beam theory. As a potential application, we demonstrate a tunable narrow band-pass filter using two electrically coupled nanomechanical arch resonators with varied dc bias voltages.